Lower bounds of Copson type for weighted mean matrices and Norlund matrices

Let 1 <= p <= infinity, 0 < q <= p, and A = (a(n,k))(n),(k >= 0)>= 0. Denote by L(p,q)(A) the supremum of those L satisfying the following inequality: (Sigma(infinity)(n=0)(Sigma(infinity)(k=0)a(n,k)x(k))(q))(1/q) >= L(Sigma(infinity)(k=0)x(k)(p))(1/p), whenever X = {x(n)}(n=0)(infinity) is an element of l(p) and X >= 0. In this article, the value distribution of L(p,q)(A) is determined for weighted mean matrices, Norlund matrices and their transposes. We express the exact value of L(p,q)(A) in terms of the associated weight sequence. For Norlund matrices and some kinds of transposes, this reduces to a quotient of the norms of such a weight sequence. Our results generalize the work of Bennett.